The spelling of Sui remained unchanged from Wade-Giles to Pinyin — even though everyone agrees that nonexperts could intuit the Chinese pronunciation more easily if the name were written the way you wrote it.

THERE ARE TWO systems of translating Chinese characters into the English language—Wade-Giles (developed in the mid-nineteenth century and used on Taiwan until 2009) and pinyin (a phonetic system developed by the Communists in the mid-twentieth century).

(Note that this can sometimes be very different in appearance from spelling used in pre-1920s texts, which will likely use the Wade-Giles system, or even some ad hoc spelling.) [See LC name authorities for form of name to use (in 100 field of authority record)]

Which of course explains why our government rejects those pinyin names the repressive government of China insists we use for Chinese cities, and instead sticks with the old Wade-Giles names or with traditional names such as Peking, Nanking, Canton, etc.